Yes, you can get the same grades of helicopter license as you can a fixed-wing license: private, commercial, and airline-transport pilot. Most people who get a commercial and an ATP also pick up an instructor rating along the way, but that is mostly orthogonal to the other three.

Ah, ok. So the classes are not very special-purpose (e.g. firefighting vs search-and-rescue), at least where you’re from.

Those are just the official FAA requirements. There are additional requirements for speciality occupations mandated by industry and insurance standards. See e.g.:

https://www.reddit.com/r/flying/comments/3zzajl/fire_pilots/